Moreover, the Schur complement
has the follwoing two
elementary properties [1]}:
\(\mathrm {det}(M) &=& \mathrm {det}(M/A) \, \mathrm {det}(A ) \quad \quad \text{(Schur formula), }  \\\mathrm {rk}(M) &=& \mathrm {rk}(M/A) + \mathrm {rk}(A) \quad \quad \text{(Guttman rank additivity formula). } \) 
